The Magpies host the North West Counties League side at Victory Park, with Hesketh hoping to secure a first qualifying round place.
He said: "We probably start as favourites being a division in front of them, but we are a new side still finding our feet.
"We got our first win of the season at Radcliffe Borough on Monday, which was a fantastic result and a big confidence-booster.
"We gave a very competent performance against Radcliffe and the signs were there that the team is beginning to gel.
"The FA Cup is something different, and every chairman and board of directors at this level will be licking their lips at the prospect of cash coming in.
"I will be warning my players there is a shock result in every round and to make sure that's not Atherton
beating us.
"Atherton are managed by Stuart Humphreys, who was at Leigh RMI. I believe he has assembled a good side."
Magpies skipper Kieran Fletcher is set to feature after a welcome return from a knee injury at Radcliffe, as will striker Danny Nolan.
But Chris Brooks and Ashley Parillion are doubtful, while Danny Finch is striving to recover from a knock.
Hesketh added: "It would be nice to get on an FA Cup run. Getting through a few rounds would be a financial God-send.
"My record in the cup isn't brilliant, although I got Barrow to the second round 12 years ago before Wigan beat us 4-0 at Holker Street.
"I also got Netherfield to the last qualifying round, and at Lancaster we got to the first round proper. But that's about as much success as I've had."